Math 442, Week 1
Page 5. ex. 3.
b) Equation ut uxx +xu = 0 has maximal order of derivative equal to 2 so
it is second order PDE. It is linear since for u and v a solutions we get
(au+bv)t +(au+bv)x x+x(au+bv) = a(ut +ux x+xu)+b(vt +vx x+xv).
Since the rig

Math 110B: Homework 5
May 14, 2012
All problems are from Strauss, Partial Dierential Equations: An Introduction, second edition.
1
9.1.1
Find all three-dimensional plane waves; that is, all the solutions of the wave equation of the form
u(x, t) = f (k x c

Math 71
Show Your Work!
Page 1 of 4
1. (20) Complete the following denitions.
(a) A subgroup of a group G is called normal if . . .
ANS: . . . the subgroup N satises xN x1 = N for all x G.
(b) Suppose that A is a set and G is a group. Then we say G acts o